Terence Tao

November 12, 2014 - Terence Tao 11/12/2014 Views: 62,847

Terence Tao, a UCLA professor and winner of the 2015 Breakthrough Prize in Mathematics, discusses his lifelong fascination with mathematics and the mysteries of prime numbers. (6:19)

>> Stephen: MY GUEST TONIGHTIS A U.C.L.A. PROFESSOR WIDELY

REGARDED AS THE WORLD'S GREATESTLIVING MATHEMATICIAN.

I'LL ASK HIM WHAT NUMBER I'MTHINKING OF.

PLEASE WELCOME TERENCE TAO.

( CHEERS AND APPLAUSE )MR. TAO, PROFESSOR TAO, THANKS

SO MUCH FOR BEING ON.

THANKS FOR BEING HERE.

>> IT'S A PLEASURE.

>> Stephen: NOW, YOU ARE APROFESSOR OF MATHEMATICS AT

U.C.L.A.

YOU HAVE WON A FIELDS MEDAL,WHICH IS REGARDED AS THE NOBEL

PRIZE OF MATHEMATICS.

>> SOMETHING LIKE THAT.

>> Stephen: IT'S BEEN CALLEDTHAT.

YOU HAVE ONE OF THOSE THEMMacARTHUR GENIUS FELLOWSHIPS

AND YOU WON THE 2015BREAKTHROUGH PRIZE IN

MATHEMATICS, THOUGH IT'S ONLY2014. DID I JUST CHECK YOUR

MATH?>> IT'S ALL ABOUT THE FUTURE.

>> Stephen: IT'S ALL ABOUT THEFUTURE OKAY.

YOU'RE KNOWN BY SOME OF YOURCOLLEAGUES AS THE MOZART OF

MATH.

HOW OLD WERE YOU WHEN YOU GOTINTO MATH?

>> SO MY PARENTS TOLD ME WHEN IWAS TWO THEY FOUND ME

TEACHING SOME OLDER KIDSHOW TO COUNT USING NUMBER BLOCKS

>> Stephen: REALLY. SO YOU'REBOSSY, TOO?

>> I GUESS SO.

I DON'T REMEMBER IT MYSELF.

APPARENTLY I TAUGHT MYSELF TOCOUNT FROM "SESAME STREET."

>> Stephen: WAS THE COUNT VONCOUNT THE ONE WHO TAUGHT YOU?

>> I GUESS IT MUST HAVE BEEN.

GOOD GUY.

>> Stephen: HE SHOULD GET SOMEOF THAT FIELDS MEDAL MONEY, I

THINK.

YOU HAVE A VERY SPECIFICSPECIALTY WHICH IS PRIME

NUMBERS.

I REMEMBER, OBVIOUSLY, IREMEMBER MATH CLASS THERE'S THE

NUMBER LINE AND ALL THAT.

POSITIVE IS THAT WAY, NEGATIVEIS THAT WAY.

TALK TO ME ABOUT PRIMES.

WHY DO I NEED TO KNOW ABOUTPRIMES?

>> PRIME NUMBERS ARE WHOLENUMBERS BIGGER THAN 1 BUT THEY

CAN'T BE FACTORED INTO SMALLERNUMBERS.

THEY'RE THE ATOMIC ELEMENTS OFNUMBER THEORY.

IN CHEMISTRY -->> Stephen: WHAT DO YOU MEAN

ATOMIC ELEMENTS

>> IN CHEMISTRY ALL MATTER ISMADE UP OF ATOMS, AND IN MATH

ALL NUMBERS ARE MADE UP OF WHOLENUMBERS LIKE 15 IS 3 TIMES 5

EVERY NUMBER CAN BE -->> Stephen: I WANT TO CHECK

THE MATH ON THAT ONE.

HOLD ON.

3... THAT CHECKS OUT.

ALL RIGHT, SO?

>> SO THEY'RE VERY FUNDAMENTALIN MATHEMATICS.

BUT DESPITE BEING SOFUNDAMENTAL, AND THEY'VE BEEN

STUDIED SINCE THE ANCIENT GREEKSMORE THAN 2,000 YEARS AGO

THERE'S A LOT WE STILL DON'TKNOW ABOUT THEM.

>> Stephen: HOW MANY PRIMENUMBERS ARE THERE?

>> THEY GO ON FOREVER.

>> Stephen: THERE HAS TO BE ANUMBER OF THEM.

THEY'RE NUMBERS, ERGO, THEREMUST BE A NUMBER OF THEM.

>> THERE'S AN INFINITY OF THEM.

IT'S ANY NUMBER YOU WISH.

>> Stephen: BUT THERE ARE NOMORE THAN INFINITY?

>> THERE'S ONLY AN INFINITENUMBER OF THEM.

>> Stephen: ONLY AN INFINITE.

THEY ARE LIMITED BY INFINITY.

>> YES.

>> Stephen: OKAY, OKAY.

THERE'S SOMETHING CALLED TWINPRIMES.

>> YES, TWIN PRIMES ARE PAIRS OF PRIMES DISTANCED TWO

APART, ALMOST AS CLOSE AS THEYCOULD BE 5 AND 7.

11 AND 13.

THESE ARE TWIN PRIMES.

>> Stephen: WOULDN'T--WOULDN'T-- WOULDN'T A TWIN PRIME

BE 5 AND 5?

>> NO, THAT'S A PRIME TWICE.

>> Stephen: OH, REALLY?

>> YES.

>> Stephen: BUT THAT'S TWINS.

TWINS ARE THE SAME PERSON TWICE.

>> WELL -->> Stephen: 5 AND 7 TWO YEARS

IS A LONG TIME FOR THE SECONDBABY TO STAY IN THE BIRTH CANAL.

>> THAT'S TRUE.

>> Stephen: BEFORE IT COMESDOWN, OKAY?

TWINS CANNOT BE TWO DIFFERENTAGES?

>> THE ANALOGY IS A LITTLE -->> Stephen: CHECK MATE, CHECK

MATE.

>> FAIR ENOUGH YOU CAUGHT ME.

>> Stephen: I GOT YA.

>> THESE ARE PAIRS OF PRIMESWHICH ARE TWO APART.

AND WE DON'T KNOW HOW MANY THEREARE.

SO YOU ASKED HOW MANY PRIMESTHERE WERE.

THERE ARE INFINITELY MANY.

WE DON'T KNOW IF THERE AREINFINITELY TWIN PRIMES OR NOT.

THIS IS ONE OF THE OLDESTQUESTIONS IN MATHEMATICS.

>> Stephen: REALLY?>> YEAH ARE THE TWIN PRIMES

A FINITE RESOURCE OR DO THEY GOON FOREVER?

WE DON'T KNOW.

>> Stephen: WHAT'S A COUSINPRIME?

IS THERE A COUSIN-->> OH! WOW, OKAY.

( LAUGHTER )( APPLAUSE )

>> COUSIN PRIMES ARE PAIRS OFPRIMES THAT ARE FOUR APART, LIKE

7 AND 11.

THEY'RE NOT QUITE AS CLOSE ASTWINS PUT THEY'RE PRETTY CLOSE.

AND THEN THERE ARE SEXY PRIMES.

>> Stephen: SEXY PRIMES?

>> SEXY PRIMES.

>> Stephen: WHAT ARE THEY?

>> THAT'S THE OFFICIAL TERM.

PAIRS OF PRIMES THAT ARE SIXAPART.

SO WE DON'T KNOW THERE ISINFINITELY MANY TWIN PRIMES.

INFINITELY MANY COUSIN PRIMES ORIF THERE ARE INFINITELY MANY

SEXY PRIMES. BUT JUST THIS YEARIT WAS PROVEN -- BASED ON A

HYPOTHESIS -- THAT ONE ONE OFTHOSE THREE CLASSES WAS

INFINITE.

>> Stephen: WAIT A MINUTE, YOUDON'T KNOW WHICH ONE IS

INFINITE, BUT YOU KNOW ONE OFTHEM IS?

>> YES.

>> Stephen: HOW COULD YOU KNOWONE OF THEM IS BUT NOT KNOW

WHICH ONE?

IS THIS LIKE "LET'S MAKE ADEAL?"

THERE ARE THREE DIFFERENTCURTAINS.

HOW DO YOU KNOW THAT?

>> THERE'S A FORMULA FOR HOWMANY TWIN PRIMES THERE ARE UP TO

A CERTAIN POINT, AND HOW MANYSEXY PRIMES OR HOW MANY COUSIN

PRIMES.

AND YOU CAN ADD THEM UP.

AND WE KNOW THE SUM IS INFINITE.ONE OF THE THREE IS INFINITE BUT

WE DON'T KNOW WHICH ONE. WE'LLPROBABLY FIGURE THEM OUT

>> Stephen: ARE COUSIN PRIMESEVER SEXY BUT YOU'RE AFRAID TO

SAY IT BECAUSE IT SOUNDS--( LAUGHTER )

( APPLAUSE )IT SOUNDS CREEPY?

>> OH, DEAR.

MAYBE SOME OF THE PRIMES, BUT,YEAH.

>> Stephen: WHAT'S YOURFAVORITE NUMBER?

( LAUGHTER )YOU'VE GOT TO HAVE ONE, RIGHT?

WHAT'S YOUR FAVORITE NUMBER?

>> IN MATHEMATICS YOU DON'T SORTOF TREAT ANY NUMBER WITH

FAVORITISM.

>> Stephen: THE BEST NUMBER IS5 BECAUSE THE JACKSON 5.

BEN FOLDS 5.

5, IT'S FIVE.>> OK

>> Stephen: WELL WHAT'S NEXT?

WHAT'S THE NEXT-- IF YOU WON THEPRIZE FOR THE FUTURE OF MATH,

WHAT'S THE NEXT THING THAT'SHAPPENING IN MATH?

>> I AM WORKING ON FLUIDEQUATIONS.

>> Stephen: ON WHAT EQUATIONS.

>> FLUID EQUATION.

>> Stephen: FOOD?

>> FLUID.

EQUATIONS THAT COVER THINGS LIKEWATER.

I'M TRYING TO FIGURE OUT IFWATER CAN SPONTANEOUSLY BLOW UP.

>> Stephen: TERENCE, THATWOULD BE GOOD TO KNOW.

>> RIGHT, RIGHT.

>> Stephen: SO GOOD LUCK WITHTHAT.

KEEP IN TOUCH, PLEASE.

>> OKAY.

>> Stephen: TERENCE TAO, THANKYOU SO MUCH.

U.C.L.A. MATHEMATICS PROFESSOR,TERENCE TAO.

PRIME NUMBERS.

WE'LL BE RIGHT BACK.